73.1.14 problem 3 (ii)

Internal problem ID [19787]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 3 (ii)
Date solved : Thursday, October 02, 2025 at 04:43:31 PM
CAS classification : [_separable]

\begin{align*} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=1+2*x(t)+(-t^2+4)*diff(x(t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {1}{2}+\frac {\sqrt {t -2}\, c_1}{\sqrt {t +2}} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 34

ode=(1+2*x[t])+(4-t^2)*D[x[t],t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\frac {1}{2}-\frac {c_1 (t-2)}{\sqrt {4-t^2}}\\ x(t)&\to -\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((4 - t**2)*Derivative(x(t), t) + 2*x(t) + 1,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1} \sqrt {t - 2}}{\sqrt {t + 2}} - \frac {1}{2} \]